Wavefront characterization of corneas

ABSTRACT

Apparatus for determining if a cornea (whether in vitro or in vivo) has been modified (either surgically or otherwise). The method includes the steps of: passing a beam of collimated light a (either coherent or incoherent) through the cornea to produce a distorted wavefront; determining the characteristics of the distorted wavefront; and analyzing the distorted wavefront for characteristics that identify the presence of a modification. The analysis of the distorted wavefront can be for the presence of higher order aberrations, or Gausian characteristics which are indicative of modifications. More particularly, the method includes the steps of providing an optical system that has a pupil plane and an image plane at a detector; positioning the cornea in the pupil plane; passing a collimated beam of light through the cornea to produce at least two images in the image plane; determining the characteristics of the distorted wavefront; and analyzing the distorted wavefront for characteristics that identify the presence of a modification. The apparatus includes: a source of collimated light: an optical system including a distorted grating and an imaging lens (which have a pupil plane, first and second virtual planes, and an image plane); structure for positioning the cornea in the pupil plane; and a computer. The structure for positioning the cornea (which is immersed in a suitable storage fluid) includes first and second piano/piano lenses. The first and second piano lens, which are substantially and perpendicular to and centered with respect to the axis, have less than λ/10 total distortions.

FIELD OF THE INVENTION

[0001] This invention relates to the use of wavefront sensing todetermine whether or not a cornea has been altered (due to correctivesurgery, or accident). More specifically, the present invention relatesto the use of wavefront sensing using a distorted defraction grating toidentify corneas (whether in vitro or in vivo) that have been surgicallymodified (e.g., radical keratotomy (RK), excimer laser photorefractivekeratectomy (PRK), laser-assisted in situ keratomileusis (LASIK) andautomated lamellar keratoplasty (ALK)).

BACKGROUND OF THE INVENTION

[0002] In the United States about 40,000 corneal transplant operationsare performed each year. While success of such surgery may depend upon anumber of other factors, one factor that always has an effect on theoutcome is the condition of the donor cornea. In the United States, adonor cornea must be transplanted within 7 days of harvesting. Outsidethe United States donor corneas may be used up to 14 days afterharvesting. Additionally, it is essential to use only corneas which havenot been modified (e.g., the subject of photorefractive surgery).

[0003] The growth of refractive surgery over the last five years hasbeen dramatic. In the August 2000 issue of Archives of Ophthalmology, P.J. McDonnell, M.D. states that this year alone over 1,500,000 refractiveprocedures will be performed. As beneficial as these procedures are, theindividual corneas are permanently altered, which makes them unsuitablefor corneal transplanting.

[0004] The increase in refraction surgery increases the likelihood thata modified cornea will be harvested for transplant purposes.Unfortunately, it is generally not possible to conclusively tell, eithervisually or under a microscope, whether such a donor cornea has beensubjected to a surgical procedure or otherwise altered.

[0005] Even when properly stored in a container (e.g., a ChironOphtholmics cornea container) filled with Optisol® or anotherappropriate solution, a donated cornea changes optically in the 14 daytime period referenced above. The interior starts to develop opticalscatter sources and the optical power of the cornea changes . Thescatter resources manifest themselves as randomly distributed opticalaberrations which increase over time. It is believed that this is causedby the cells of the harvested cornea not being able to reject wastematerial. The change in optical power is believed to be caused by anoverall relaxation of the tissue. Regardless of the cause, the netresult is that these aberrations produce scintillation and staticaberrations when a beam of light is passed through a donated cornea.

[0006] PCT/GB99/00658 (International Publication No. WO 99/467768),based on applications filed in Great Britain on Mar. 10, 1998 and Dec.23, 1998, discloses a three dimensional imaging system including a lensand a distorted diffraction grating which images objects located atdifferent distances from the grating simultaneously and spatiallyseparated in a single image plane. The grating is distorted according toa quadratic function so as to cause the images to be formed underdifferent focus conditions. It is stated that the system is useful forsimultaneously imaging multiple layers within a three dimensional objectfield, and has applicability in a number of fields including opticalinformation storage, imaging short-time scale phenomena, microscopy,imaging three dimensional object structures, passive ranging, laser beamprofiling, wavefront analysis, and millimeter wave optics. The abilityto make wavefront measurements is not disclosed or claimed.

[0007] P. M. Blanchard et al., “Multi-Plane Imaging With a DistortedGrating,” Proceedings of the 2nd International Workshop on AdaptiveOptics for Industry and Medicine, World Scientific, pp. 296-301, Jul.12-16, 1999, describe a technique for simultaneously imaging multiplelayers within an object field onto the detector plane of a singledetector. The authors, who are the named inventors in PCT/GB99/00658,state that the imaging of multiple layers within an object field is“useful in many applications including microscopy, medical imaging anddata storage.” (See page 296.) The apparatus includes the use of abinary diffraction grating in which the lines are distorted such at eachdifferent level of defocus is associated with each diffraction order.When such a grating is placed in close proximity to a lens, the gratingcreates multiple foci of the image. This multi-foci effect enables theimaging of multiple object planes onto a single image plane.

[0008] L. J. Otten et al. “3-D Cataract Imaging System,” Proceedings ofthe 2nd International Workshop in Adaptive Optics for Industry andMedicine, World Scientific, pp. 51-56, describe optics and an associateddiagnostic system for volumetric, in vivo imaging of the human lens tocharacterize or grade cataracts. The described method and apparatus arebased on the use of a distorted grating (of the type disclosed inPCT/GB99/00658 and the Blanchard et al. paper, supra) in conjunctionwith a focusing lens and a re-imaging lens. (See FIG. 1 of thisreference.) The quadratic phase shift, introduced by the grating, leadsto a different degree of defocus in all diffraction orders, whichproduces a series of images of different layers of the cataract, eachwith different defocus conditions, simultaneously and side-by-side onthe detector. Thus, in-focus images of different object planes areproduced.

[0009] Analysis of the optical images referenced above requires the useof the Intensity Transport Equation (I.T.E.) and the employment of aGreen's function to produce a wavefront map. S. Woods, P. M. Blanchardand A. H. Greenaway, “Laser Wavefront Sensing Using the IntensityTransport Equation,” Proceedings of the 2nd International Workshop onAdaptive Optics for Industry and Medicine, World Scientific, pp.260-265, Jul. 12-16, 1999, describe both the I.T.E. and a Green'sfunction solution thereto in conjunction with laser wavefront sensing.

OBJECT OF THE INVENTION

[0010] It is an object of the present invention to determine, withwavefront sensing, whether or not a cornea has been altered (eitherdeliberately or accidentally).

[0011] It is another object of the present invention to determine, withthe use of wavefront sensing using a distorted grating, those donorcorneas that have been modified by surgery or other methods.

[0012] It is another object of the present invention to provide a simpleoptical system (particularly including a light source, an imaging lens,a distorted grating and a data camera) to form, in the detector plane,images from which wavefront aberrations in the cornea can be derived.The beam of light that passes through a cornea (located in the pupilplane) and two virtual planes on opposite sides of and equidistant fromsuch pupil plane.

[0013] It is an additional object of the present invention to provide aholder for a donor cornea which does not mask optical data from suchcornea.

[0014] It is yet another object of the present invention to provide aholder for a donor cornea that has optical windows that aresubstantially free of distortion which would mask corneal optical data.

[0015] It is yet still another object of the present invention in whichthe optical windows have less than λ/10 distortions.

[0016] These and other objects will be apparent from the descriptionwhich follows.

SUMMARY OF THE INVENTION

[0017] A method of determining if a cornea (whether in vitro or in vivo)has been modified (either surgically or otherwise). The method includesthe steps of: passing a beam of collimated light a (either coherent orincoherent) through the cornea to produce a distorted wavefront;determining the characteristics of the distorted wavefront; andanalyzing the distorted wavefront for characteristics that identify thepresence of a modification. The analysis of the distorted wavefront canbe for the presence of higher order aberrations, or Gausiancharacteristics which are indicative of modifications. Moreparticularly, the method includes the steps of providing an opticalsystem that has a pupil plane and an image plane at a detector;positioning the cornea in the pupil plane; passing a collimated beam oflight through the cornea to produce at least two images in the imageplane; determining the characteristics of the distorted wavefront; andanalyzing the distorted wavefront for characteristics that identify thepresence of a modification.

[0018] The apparatus for determining whether a cornea has beensurgically modified includes: a source of collimated light, an opticalsystem including a distorted grating and an imaging lens (which have apupil plane, first and second virtual planes, and an image plane);structure for positioning the cornea in the pupil plane; means forrecording the images of the first and second virtual planes; means fordetermining from the first and second images the distorted wavefront;and means for analyzing said wavefront for characteristics indicative ofmodified corneas. The first and second virtual planes are on oppositesides of and equally spaced from said pupil plane.

[0019] The structure for positioning the cornea (which is immersed in asuitable storage fluid) is a container which includes: a housing havingfirst and second ends; structure positioned within the housing forsupporting the perimeter of the cornea; a first plano/plano lens forclosing the first end of the housing; and a cap for closing the secondend of the housing. The cornea support is substantially symmetrical withrespect to an optical axis. The first plano/plano lens is substantiallyperpendicular to the optical axis. Finally, the cap includes a secondplano/plano lens which is substantially parallel to the first pianolens. The first and second plano/plano lens, which are substantiallycentered with respect to the axis, have less than λ/10 totaldistortions. The support structure includes a cage and a pedestal withthe cage being supported by the pedestal. Preferably, the cage andpedestal are integrally formed with the housing. Finally, the cap has atop portion and a skirt which axially inwardly spaces the second lensfrom the top portion to create an annular area where air will collectwhen the container is holding a cornea and fluid, so that air will notinterfere with a beam of light passing through the first and secondplano/plano lenses and cornea.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020]FIG. 1 is a schematic of the optical system of the instrument tocharacterize donor corneas;

[0021]FIG. 1A is the front view of the distorted grating used in theinstrumentation to characterize corneas;

[0022]FIG. 1B is the front view of the detector plane of the detector ofthe instrumentation to characterize corneas, and the images in suchplane;

[0023]FIG. 2 is a cross-section view of an optical cornea container ofthe present invention;

[0024]FIG. 3 is a cross-sectional, perspective view of an improvedcornea container of the present invention;

[0025]FIG. 4 is a cross-sectional view of the improved optical corneacontainer of FIG. 3 in the open position;

[0026]FIG. 4A is a cross sectional view of the improved optical corneacontainer of FIG. 3 in the closed position.

[0027]FIG. 5 is a diagram showing the baseline date of the system ofFIG. 1, with no cornea or container;

[0028]FIG. 6 is a diagram showing the baseline date of the system of

[0029]FIG. 1, with the container of FIG. 2 filled with Optisol®, butwith no cornea;

[0030]FIG. 7 is a diagram showing the data from an unmodified cornea L,held in the container of FIG. 2, positioned in the pupil plane of FIG.1, and exposed to coherent and collimated light;

[0031]FIG. 8 is a diagram showing the data from a an unmodified corneaR, held in the container of FIG. 2, positioned in the pupil plane ofFIG. 1, and exposed to coherent and collimated light;

[0032]FIG. 9 is a diagram showing the data from cornea L after it hasbeen surgically modified, again held in the container of FIG. 2,positioned in the pupil plane of the system of FIG. 1, and exposed tothe same coherent and collimated light;

[0033]FIG. 10 is a diagram showing the data from the cornea R after ithas been surgically modified, again held in the container of FIG. 2,positioned in the pupil plane of FIG. 1, and exposed to the samecoherent and collimated light;

[0034]FIG. 11 is a three dimensional presentation of the data set forthin FIG. 7;

[0035]FIG. 12 is a three dimensional presentation of the data set forthin FIG. 8;

[0036]FIG. 13 is a three dimensional presentation of the data set forthin FIG. 9;

[0037]FIG. 14 is a three dimensional presentation of the data set forthin FIG. 10;

[0038]FIG. 15 is a three dimensional presentation of the wavefront ofcornea LL which was modified by a LASIK procedure (prior to the death ofthe donor), held in the container of FIG. 2, positioned in the pupilplane of FIG. 1, and exposed to coherent, illuminated light;

[0039]FIG. 16 is a three dimensional presentation of the wavefront ofcornea LR which was modified by a LASIK procedure (prior to the death ofthe donor), held in the container of FIG. 2, positioned in the pupilplane of FIG. 1, and exposed to coherent, illuminated light; and

[0040]FIG. 17 is a schematic of the optical system used to characterizein vivo corneas.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0041] With reference to FIG. 1, the apparatus 11 for determiningwhether an in vitro cornea has been modified (either surgically orotherwise) includes a source of collimated coherent light 13, a corneacontainer 15, a distorted diffraction grating 17, a high quality imaginglens (or lens set) 19, and a detector 21 (either film or electronic)having a detector plane 23. (Grating 17, lens 19 and detector 21 aresometimes referred to as wavefront sensor 24.) Apparatus 11 alsoincludes a beam path 25, a pupil plane 27, first virtual plane 29,second virtual plane 31, and a computer 33. Computer 33 is connected todetector 21, via a data acquisition device such as a frame grabber(located within the computer housing). Computer 33 stores the imagesform detector 21, determines the wavefront from the stored images, andthe analyzes the wavefront for the characteristics that identify analtered cornea (e.g. compares the wavefronts to a stored norm). Therepresentation of the virtual planes between source 13 and sensor 24 isfor convenience only. In the preferred embodiment they are 73 cm oneither side of pupil plane 27. Source 13 is a coherent laser such as a633 nm HeNe laser. As those skilled in the art will appreciatenon-coherent sources, such as spectrally band filtered white light,could also be used.

[0042] With grating 17 in close proximity to lens 19 (typically thesetwo elements would, in fact, be in contact with each other along beampath 25), the 0, +1 and −1 diffraction orders of grating 17 image pupilplane 27, virtual object plane 29 and virtual object plane 31 ontodetector plane 23. The higher order diffraction orders are cut off by anappropriately placed field stop so as not to contaminate the image ofthe 0 and +1 and −1 orders. Further, with the zero order being an imageof the pupil plane 27, the images in the +1 and −1 diffraction orderscorrespond to virtual image planes equidistant from and an oppositesides of pupil plane 27. The grating is distorted according to,${\Delta_{x}\left( {x,y} \right)} \eqsim {\frac{W_{20}d}{\lambda \quad R^{2}}\left( {x^{2} + y^{2}} \right)}$

[0043] where λ is the optical wavelength, x and y are Cartesianco-ordinates with an origin on the optical axis and R is the radius ofthe grating aperture which is centered on the optical axis. Theparameter W₂₀, defines the defocusing power of the gratings, and is thestandard coefficient of the defocus equivalent on the extra pathlengthintroduced at the edge of the aperature, in this case for the wavefrontdiffracted into the +1 order. The phase change (Ø_(m)) imposed on thewavefront diffracted into each order m is given by,${\phi_{m}\left( {x,y} \right)} = {m\frac{2\quad \pi \quad W_{20}}{\lambda \quad R^{2}}\left( {x^{2} + y^{2}} \right)}$

[0044] The various containers in which donor corneas are stored areunusable for optical diagnostics. The aberrations produced by the wallsof such containers mask the aberrations exhibited by corneas bothunaltered and altered. With reference to FIG. 2, optical corneacontainer 15 includes cylindrical housing 41, first optical window 43,second optical window 45, and fluid containment ring 47. Housing 41 andring 47 are concentric rings, both bonded to optical window 43. Window43 is a plano/plano lens having surfaces 49, 51 which are substantiallyconcentric with respect to beam path 25 and substantially perpendicularthereto. Similarly, window 45 is a plano/plano lens having surfaces 53,55 which are also substantially concentric with and substantiallyperpendicular to beam path 25. Collectively, windows 43 and 45,including surfaces 49, 51 and 53, 55 have total aberrations of less thanλ/10. In operation, cavity 57 is filled with Optisol®, or anothersolution suitable for the storage of donor corneas, to the top ofhousing 41 so that the meniscus causes such fluid to slightly over fillcavity 57. Window 45 is then slid over housing 41 without trapping anyair in cavity 57. Excess fluid is collected between housing 41 and ring47.

[0045] With reference to FIGS. 3 and 4, improved cornea container 15 ¹includes a cylindrical body portion 61, a cornea support cage portion63, and a cap portion 65. Body portion includes a bottom surface 67, anupper skirt portion 69 having a groove 71 therein for supporting ano-ring seal 73 and threads (not shown), and a cavity 74. Body portion 61also includes a conical shaped skirt 75 integral with bottom surface 67for centrally positioning cage portion 63 within body portion 61 asillustrated in FIGS. 3 and 4. Cage portion 63 includes a plurality offingers 77, which are supported by ring portion 79 of skirt 75 in acylindrical pattern concentric with axis 81. As best illustrated in FIG.4, the free ends of fingers 77 include, inter alia, an inwardly slopingbevel 83 and notch 84 for supporting a donor cornea, such as illustratedat 85. Finally, body portion 61 includes a piano/piano lens 87 securedto ring portion 79. Lens 87 has parallel piano surfaces 89 and 91 whichare substantially centered with respect to axis 81 and substantiallyperpendicular thereto. Cap portion 65 includes a skirt portion 93, ashoulder 95 which seats against 73, a top portion 96, and an inner skirtportion 97 having a circumferential lip 99. Inner surface 100 includesthreads (not shown) which mate with the threads (also not shown) onskirt 69. Secured to lip 99 is a second piano/plano lens 101 havingpiano parallel surfaces 103 and 105. When cornea container 15′ isclosed, with seal 73 received in circumferential recess 95, surfaces 103and 105 are substantially centered with respect to to axis 81 andsubstantially perpendicular thereto. Collectively, the aberrations inlenses 87 and 101, including surfaces 89, 91, 103 and 105, have a totalaberration of less than λ/10.

[0046] In operation, donor cornea 85 is placed in cage 63, with aportion of the convex surface thereof in contact with bevels 83 and theperimeter received within notches 84. In this position, donor cornea issubstantially centered about axis 81. Cavity 74 is then filled with asuitable storage fluid and capped by screwing on cap 65. As can be seenfrom FIG. 4A, because inner skirt portion 97 projects inwardly, closureof cap 65 will force excess fluid out of cavity 74. In the event thatthere is any under filling of cavity 74, any air which might be trappedin cavity 74 is collected in annular area 107 (outside of the beampath).

[0047] With nothing in pupil plane 27 of apparatus 11 (e.g., corneacontainer 15 removed) and source 13 present, the images recorded ondetector plane 23 are as illustrated in FIG. 1B. Data was collectedwithout any disturbances (i.e., no cornea container, cornea storagesolution, or cornea) to determine the residual errors in the optics and,thus, establish the base line for instrument 11. With reference to FIG.5, the raw images as recorded by detector 21 are shown along with thereduced Zernike terms, annotated to show where the various types of dataare located in the figure. All the data are taken using a 633 nanometerHeNe laser as the illumination source. Most of the error is tip andtilt, which is the result of not accurately aligning wavefront sensor 24and for not accurately accounting for where the distorted grating imageswere actually placed on detector plane 23. These two terms can be madeequal to zero by: (1) subtracting them in the analysis of the wavefrontto accommodate images that are not exactly centered on the same line; or(2) a more precise alignment of wavefront sensor 24. The otheraberrations (e.g. focus) are seen to be small, on the order of or lessthan 0.1λ. All the baseline aberrations, including tip and tilt, can besubtracted from the cornea data.

[0048] Next, a baseline for optical system 11, with cornea container 15located in pupil plane 27 and cavity 57 filled with Optisol® solution,but without a cornea, was established. The baseline data is set forth inFIG. 6. Again, all aberrations can be compensated for or eliminatedusing the criteria set forth above with regard to FIG. 5.

[0049] After establishing the baseline, an unmodified donor cornea L wasplaced in cornea container 15, centered as illustrated in FIG. 2, filledwith Optisol® solution, and then closed with optical window 45 in themanner set forth above. Container 15 was then placed in instrument 11,in optical beam path 25 and with cornea L in pupil plane 27, asillustrated in FIG. 1. If necessary, predetermined aberrations can beintroduced into the beam path prior to the beam reaching the pupil planeand subsequently accommodated in the analysis of the data. The measurederrors are illustrated in FIG. 7. In this figure the tip and tilt termsare irrelevant since they are associated with cornea container 15 and,the orientation of cornea L therein. Cornea L is seen to have focus andastigmatism errors.

[0050] As with cornea L, cornea R was placed in container 15, andcentered as set forth above. Cavity 57 as was then filled with Optisol®and closed with optical window 45. Cornea container 15 was then placedin the pupil plane of instrument 11. The measured errors are illustratedin FIG. 8. As with cornea L, the tip and tilt terms for cornea R areirrelevant since they are associated with container 15 and the specificorientation of cornea R therein, both of which are not controlled. As isevident from FIG. 8, cornea R has focus, astigmatism and coma errors.

[0051] The data illustrated in FIGS. 7 and 8 were collected using a 12mm diameter collimated beam. The measurements were repeated with an 8mm, and 5 mm collimated beams to see if the measured aberrations werebeing effected by the irregular outer edge of the corneas. The effect ofreducing the beam size was to improve the quality of the images but atthe expense of brightness and the area examined. All data were collectedwith the beam centered on the cornea.

[0052] To demonstrate the ability of apparatus 11 to detect surgicallymodified corneas, cornea L was then modified using a PRK procedure toadd 4 diopters of focus change. Cornea R was also subjected to the sameprocedure to add 8 diopters of focus change. After modification eachcornea was, in turn, again centered in cavity 57, which was filled withOptisol® and closed, and container 15 placed in apparatus 11 with themodified cornea again in pupil plane 27.

[0053] The measured errors for cornea L (modified) are illustrated inFIG. 9. Again, tip and tilt are irrelevant since they are associatedwith cornea container 15 and the orientation of cornea L (modified)therein. Cornea L (modified) is seen to have considerably larger focusand astymatism errors then cornea L. The higher order errors (coma 1,coma 2, trifoil 1, trifoil 2 and spherical) are also considerably largerand provide one of the basis for the determination that the cornea hasbeen altered.

[0054] The measured errors for cornea R (modified) are illustrated inFIG. 10. As before, tip and tilt are irrelevant. Cornea R (modified) isseen to have considerably larger focus and astymatism errors than corneaR. As with cornea L (modified) the higher order aberrations have alsoincreased (again indicating that the cornea has been modified). Asummary of the results is shown in Table 1. Note that the measureddifference (in waves) between the two corneas is a factor of 2, the sameamount of focus difference introduced by the PRK procedure. TABLE 1Focus Term Before Focus Term After Difference Cornea Modification(waves) Modification (waves) (waves) L 1.77 3.23 1.46 R 1.024 4.1323.108

[0055] An alternative way of illustrating the data set forth inconjunction with FIGS. 7-10 is to present the distorted wavefrontsproduced by the respective unaltered and altered corneas as threedimensional images. This type of presentation is illustrated in FIGS.11-14, wherein: FIG. 11 corresponds to FIG. 7; FIG. 12, to FIG. 8; FIG.13, to FIG. 9; and FIG. 14, to FIG. 10. In FIGS. 11-16, the grey scaleon the right is a representation of the distortion. Note thesimilarities of the Gaussian-like slope of the wavefront aberrationsmeasured for the modified corneas, which provides another basis fordetermining whether a cornea has been modified.

[0056] Right (RL) and left (LL) corneas from a donor who had the LASIKcorrective surgery prior to death were measured in the same manner asthe unmodified corneas L and R (FIGS. 7 and 8) and the PRK modifiedcorneas (FIGS. 9 and 10). FIG. 15 is the left (LL) LASIK modifiedcornea. FIG. 16 is the right (RL) LASIK modified cornea. Thecharacteristics Gausian-like shape of the wavefront produced by thelaser surgery is clearly present in both corneas. As with the PRKmodified corneas (FIGS. 9 and 10), the hier order aberrations areconsiderably larger than those aberrations in the unmodified corneas(FIG. 7 and 8).

[0057] The basis for extracting the wavefront from the data collectedfrom detector 21 is to solve the Intensity Transport Equation (I.T.E.).The I.T.E. is derived by expressing the parabolic wave equation forcomplex amplitude in terms of intensity (1) and phase (Ø), and relatesto the rate of change of intensity in the direction of the propagationto the transverse gradient and La Placian of the phase:${{- \frac{2\pi}{\lambda}}\frac{\partial I}{\partial z}} = {{I\quad {\nabla^{2}\phi}} + {{\nabla\quad I} \cdot {\nabla\quad \varphi}}}$

[0058] For a uniformly illuminate aperture, R, with perimeter P, the ITEsimplifies to${\frac{2\pi}{\lambda}\frac{1}{I_{o}}\frac{\partial I}{\partial z}} = {{W_{R}{\nabla^{2}\phi}} - {\delta_{P}\frac{\partial\varphi}{\partial\eta}}}$

[0059] where W_(R) is the aperture function (=1 inside R, =0 outside R),δ_(p) is a delta-function around P, and ∂φ/∂η is the normal derivativeof φ on P.

[0060] Consider the problem of finding the phase at a particular pointr. We can express this in terms of an integral involving adelta-function as follows:

φ(r)=∫_(R)φ(r′)δ(r−r′)

[0061] If we have a Green's function satisfying${{\nabla^{2}{G\left( {r,r^{\prime}} \right)}} = {\delta \left( {r - r^{\prime}} \right)}},{{\frac{\partial{G\left( {r,r^{\prime}} \right)}}{\partial\eta}_{P}} = 0}$

[0062] then we can say

φ(r)=∫_(R)φ(r′)∇² G(r,r′)

[0063] Applying Green's 2^(nd) identify;${\varphi (r)} = {{\int_{R}{{G\left( {r,r^{\prime}} \right)}{\nabla^{2}{\varphi \left( r^{\prime} \right)}}}} + {\oint_{P}{{\varphi \left( r^{\prime} \right)}\frac{\partial{G\left( {r,r^{\prime}} \right)}}{\partial\eta}}} - {\oint_{P}{{G\left( {r,r^{\prime}} \right)}\frac{\partial{\varphi \left( r^{\prime} \right)}}{\partial\eta}}}}$

[0064] and the boundary condition on the Green's function;$\begin{matrix}{{\varphi (r)} = {{\int_{R}{{G\left( {r,r^{\prime}} \right)}{\nabla^{2}{\varphi \left( r^{\prime} \right)}}}} - {\oint_{P}{{G\left( {r,r^{\prime}} \right)}\frac{\partial{\varphi \left( r^{\prime} \right)}}{\partial\eta}}}}} \\{= {\int_{R}{{G\left( {r,r^{\prime}} \right)}\left( {{\nabla^{2}{\varphi \left( r^{\prime} \right)}} - {\delta_{P}\frac{\partial{\varphi \left( r^{\prime} \right)}}{\partial\eta}}} \right)}}}\end{matrix}$

[0065] we get the solution. The term in parenthesis is the right handside of the ITE. The wavefront phase is thus obtained by measuring theintensity derivative (the left hand side of the ITE), multiplying by theGreen's function and integrating;${\varphi (r)} = {{- \frac{2\pi}{\lambda}}\frac{1}{I_{o}}{\int_{R}{{G\left( {r,r} \right)}^{\prime}\frac{\partial{I\left( r^{\prime} \right)}}{\partial z}}}}$

[0066] The intensity derivative,$\frac{\partial{l\left( r^{\prime} \right)}}{\partial z}$

[0067] is obtained by the subtraction of two pixellated images. TheGreen's function is be pre-calculated on the appropriate grid and thesolution obtained by the matrix multiplication:$\varphi = {{- \frac{2\pi}{\lambda}}\frac{1}{I_{o}}{\sum\limits_{J}{{Gi}_{j}\left( \frac{\partial I}{\partial z} \right)}_{j}}}$

[0068] The particular solution will vary, depending on the specifics ofthe optical design, the detector and the distorted crating used.

[0069] While the foregoing has dealt with donor corneas, the same basicprocedure can also be used on in vivo corneas. With reference to FIG.17, system 111 includes a source of collimated coherent light 113, abeam splitter 115, a distorted diffraction grating 117, a high qualityimaging lens or lens set 119. and a detector 121 (either film orelectronic) having a detector plane 123. As with instrument 11, grating117, lens 119 and detector 121 constitute wavefront sensor 124. System111 also includes a beam light 125, a pupil plane 127, a first virtualplane 129, a second virtual plane 131, and a computer 133 connected todetector 121 by a data acquisition device, such as a frame grabberlocated within the computer housing. As with the first embodiment,source 113 is a coherent laser whose energy, when projected into the eyemeets FDA approved eye safe levels. Grating 117, which is also distortedaccording to the grating equation set forth above, is in close proximitywith or touching lens 119. System 111 also includes apparatus, notshown, for positioning the patient's head such that his/her cornea is inpupil plane 127.

[0070] In operation the beam from source 113 is directed through beamsplitter 115, through the cornea 125 and of eye 127, onto the retina 129where it is reflected back through the cornea and then directed. by beamsplitter 115 to wavefront sensor 124. As with instrument 11, the 0, +1and −1 diffraction orders of grating 117 image pupil plane 127, virtualobject plane 129 and virtual object plane 131 onto detector plane 123.Again, the higher order diffraction orders are cut off by anappropriately placed field stop so as not to contaminate the image ofthe 0 and +1 and −1 orders. Further, with zero order being an image ofthe pupil plane 127, the images in the +1 and −1 diffraction orderscorrespond to virtual image planes equidistant from and opposite sidesof pupil plane 127. Computer 133 stores the images from detector 121,determines the wavefront from the stored images in the manner set forthabove with the I.T.E. and a Green's function, and then analyzes thewavefront for the characteristics that identify an altered cornea (e.g.,compares the wavefront to a stored norm).

[0071] Whereas the drawings and accompanying description have shown anddescribed the preferred embodiment of the present invention, it shouldbe apparent to those skilled in the art that various chances may be madein the form of the invention without affecting the scope thereof.

We claim
 1. A method of determining whether a cornea is abnormal, saidmethod including the steps of: a. passing a beam of collimated lightthrough said cornea to produce a wavefront modified by said cornea; b.measuring said modified wavefront; and c. analyzing said measured,modified wavefront for features that identify the presence of a cornealabnormality.
 2. The method of claim 1, wherein said analysis is for thepresence of higher order optical aberrations.
 3. The method of claim 2,wherein said analysis is for the presence of residual grating-likeoptical aberrations, said optical aberrations being indicative ofsurgical modification.
 4. The method of claim 1, wherein said analysisis for the presence of Gausian characteristics which are indicative ofsurgical modification.
 5. The method of claim 1, wherein said step forpassing said beam of collimated light is accomplished with coherentlight.
 6. The method of claim 1, wherein said step for passing said beamof collimated light is accomplished with incoherent light.
 7. The methodof claim 1, wherein said cornea is an in vitro cornea.
 8. The method ofclaim 1, wherein said cornea is an in vivo cornea.
 9. The method ofclaim 1, wherein said step of measuring includes mathematicallyproducing a representation of said modified wavefront.
 10. The method ofclaim 9, wherein measuring includes use of the Intensity TransportEquation and a Green's Function.
 11. The method of claim 1 wherein saidanalysis includes comparing said modified wavefront to a storedwavefront.
 12. Method of determining whether a cornea has been modified,said method including the steps of: a. positioning said cornea in thepupil plane of an optical system; b. passing a collimated beam of lightthrough said cornea and a distorted grating to produce, in the imageplane of said optical system, intensity maps of said pupil plane and twovirtual image planes images located on either side of said pupil plane;c. determining from said images, the wavefront of said light after ithas passed through, and been modified by, said cornea; and d. analyzingsaid modified wavefront for features that identify a modified cornea.13. The method as set forth in claim 12, of wherein said intensity mapsare the zero, +1 and −1 defraction orders produced by said distortedgrating.
 14. The method as set forth in claim 13, wherein said analysisincludes the step of comparing said modified wavefront with a storednorm.
 15. The method as set forth in claim 13, wherein said modifiedwavefront is determined from said images, the Intensity TransportEquation and a Green's function.
 16. The method of claim 15, whereinsaid analysis of said modified wavefront is to determine the presence ofhigher order aberrations.
 17. The method of claim 16, wherein saidanalysis of said modified wavefront is to determine the presence ofgrating like features which are indicative of a particular type ofsurgical modification.
 18. The method of claim 15, wherein said analysisof said modified wavefront is to determine the presence of Gausiancharacteristics which are indicative of modifications.
 19. The method ofclaim 12, further including the step of introducing predeterminedmodifications into said collimated beam of light prior to said beam oflight passing through said cornea to increase the dynamic range of saiddetermination.
 20. Apparatus for determining whether a cornea has anabnormality, said apparatus comprising: a. a source of collimated lighthaving known wavefront characteristics; b. an optical system includingan optical path, a distorted grating and lens means, said optical systemalso including pupil plane, first and second virtual planes, and animage plane, said first and second virtual planes being on oppositesides of and equally spaced from said pupil plane; c. means forpositioning said cornea in said pupil plane; d. means for focusingpositioning said virtual planes in said image plane, and means forrecording the images of said first and second virtual planes; e. meansfor determining from said images of said first and second virtual planesimages the wavefront of said source after it has passed through and beenmodified by said cornea; and f. means for analyzing said modifiedwavefront for features indicative of a cornea with an abnormality. 21.The apparatus of claim 20, wherein said means for positioning saidcornea includes a container having first and second optical windows, andmeans for positioning said container and said optical windows in saidoptical path.
 22. The apparatus of claim 21, wherein said container isat least partially filled with a suitable cornea preservation media. 23.The apparatus of claim 20, wherein said means for positioning saidcornea includes apparatus for positioning a patient's head such thathis/her cornea is in said pupil plane.
 24. The apparatus of claim 20,wherein said means for determining said modified wavefront includesmeans for producing a mathematical representation of said modifiedwavefront.
 25. The apparatus of claim 24, wherein said means forproducing said mathematical representation includes a computer, theIntensity Transport Equation and a Green's Function.
 26. The apparatusof claim 25, wherein said means for analyzing said modified wavefrontalso includes means for storing said images.
 27. The apparatus of claim26, wherein said means for analyzing includes a stored norm.
 28. Themethod as set forth in claim 13, wherein said virtual image planes areequally spaced from said pupil plane.
 29. A. method of determining thecharacteristics of measuring a scintillated wavefront, said methodincluding the steps of: a. passing a collimated collimating the opticalbeam of light containing said scintillated the wavefront through anoptical system including to be measured and a distorted grating, anobject plane and an image plane, to produce three images in said theimage plane of said optical system; b. positioning said scintillatedwavefront in said pupil plane; c. determining, from said images, thewavefront of said scintillated wavefront; and d. analyzing saiddetermined scinitillated wavefront for features that characterize saiddetermined scintillated the wavefront.
 30. The method as set forth inclaim 29, of wherein said images are the zero, +1 and −1 diffractionorders of said distorted grating.
 31. The method as set forth in claim29, wherein said scintillated wavefront is determined mathematically bythe use of said images, the Intensity transport Equation and a Green'sfunction.
 32. The apparatus for measuring a said scintillated wavefront,said apparatus comprising consisting of: a. an optical system includingan optical path, a method for collimating said light beam, a distortedgrating and a lens means, said optical system also having a pupil plane,first and second virtual planes, and an image plane, said first andsecond virtual planes being on opposite sides of and equally spaced fromsaid pupil plane; b. means for positioning said scintillated wavefrontin said pupil plane; c. means, positioned in said image plane, forrecording the images in said first and second virtual planes; d. meansfor determining from said first and second images said scintillated thewavefront of said collimated scintillated; and e. means for analyzingsaid determined scintillated wavefront after it has passed through saidcornea for features that characterize said determined indicative of thewavefront characteristics under scintillated wavefront.